Ethereum: Why is no security lost by using 32-byte public keys in Schnorr signatures instead of 33?

I can provide you with an article on this topic. However, I need to clarify that there isn’t a specific discussion or question about truncating 33-byte public keys from Schnorr signatures in Ethereum.

That being said, here’s a draft article based on my understanding of the topic:

Ethereum: Why No Security Loss Occurs with 32-Byte Public Keys and Schnorr Signatures

Public keys are the unique identifiers for digital assets, allowing users to securely access their cryptographic keys. In Ethereum, public keys are represented as (x, y) coordinates, where x represents the private key and y represents the associated public key.

When it comes to Schnorr signatures, a type of digital signature used in Ethereum transactions, there is currently a discussion about using 32-byte public keys instead of the standard 33-byte format. Specifically, some users are asking why no security loss occurs when using shorter public keys.

What are Schnorr Signatures?

Schnorr signatures are a type of digital signature that allows users to sign messages without revealing their private key. They use a one-way hash function and a secret number called the “secret value” (s) to create a unique identifier for each message. This identifier is then used to generate a digital signature, which is hashed with the user’s private key.

The 33-byte Format

In Ethereum, public keys are typically represented as (x, y) coordinates, where x represents the private key and y represents the associated public key. The standard format for these coordinates is 32 bytes long, consisting of:

• X-coordinate: a random 256-bit value

• Y-coordinate: a random 256-bit value

The Trade-Off

When using Schnorr signatures with shorter public keys (e.g., 31-byte), some users are arguing that no security loss occurs because the shortened key is still long enough to generate the required secret values. The shortening of the key can actually improve efficiency, as it reduces the computational overhead associated with generating and verifying the digital signature.

However, this argument assumes that the shorter key is still valid and secure. In reality, the shorter key may not be valid for all cryptographic operations, such as encryption or signing large messages. Additionally, some users may argue that using a longer key provides more flexibility and reliability when it comes to cryptographic operations.

Conclusion

While there are valid arguments both sides of this discussion, there isn’t a consensus yet on whether the use of 32-byte public keys in Schnorr signatures in Ethereum is secure or not. The debate is ongoing, and it’s essential for users to stay up-to-date with the latest developments and updates from the Ethereum community.

In conclusion, while using shorter public keys may provide some benefits, such as improved efficiency and flexibility, no security loss occurs when using these shortened keys. However, users should be aware of potential trade-offs and risks associated with shortening their public keys before making a decision.

Please note that this article is based on my understanding of the topic, and I’m not an expert in cryptography or Ethereum development. If you have any specific questions or concerns about Schnorr signatures or 32-byte public keys in Ethereum, feel free to ask!

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